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In the theory of stationary spatial point processes, Palm distributions are used to describe the point process seen from one of its points. Such an intrinsic frame of reference is not only interesting for theoretical considerations, but also useful in related fields such as queuing theory and stochastic geometry.

Stochastic geometry.

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The classical subjects of geometric probability and integral geometry, and the more modern one of stochastic geometry, are developed here in a novel way to provide a framework in which they can be studied. The author focuses on factorization properties of measures and probabilities implied by the assumption of their invariance with respect to a group, in order to investigate nontrivial factors. The study of these properties is the central theme of the book. Basic facts about integral geometry and random point process theory are developed in a simple geometric way, so that the whole approach is suitable for a nonspecialist audience. Even in the later chapters, where the factorization principles are applied to geometrical processes, the only prerequisites are standard courses on probability and analysis. The main ideas presented have application to such areas as stereology and geometrical statistics and this book will be a useful reference book for university students studying probability theory and stochastic geometry, and research mathematicians interested in this area.

Stochastic geometry --- Factorization (Mathematics) --- Geometric probabilities --- 519.21 --- Geometry --- Probabilities --- Mathematics --- Probability theory. Stochastic processes --- Geometric probabilities. --- Stochastic geometry. --- Factorization (Mathematics). --- 519.21 Probability theory. Stochastic processes

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This book deals with the Boolean model, a basic model of stochastic geometry for the description of porous structures like the pore space in sand stone. The main result is a formula which gives in two and three dimensions a series representation of the most important model parameter, the intensity, using densities of so-called harmonic intrinsic volumes, which are new observable geometric quantities.

Stochastic geometry --- Boolean model --- Intensitätsschätzung --- method of densities --- anisotropy --- Anisotropie --- intensity estimation --- Boolesches Modell --- Stochastische Geometrie

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Quantum mechanics. Quantumfield theory --- Quantum field theory. --- Topology. --- Stochastic geometry. --- Mathematical physics. --- Champs, Théorie quantique relativiste des. --- Topologie. --- Géométrie stochastique. --- Physique mathématique. --- Mathematical physics --- Quantum field theory --- Stochastic geometry --- Topology --- Analysis situs --- Position analysis --- Rubber-sheet geometry --- Geometry --- Polyhedra --- Set theory --- Algebras, Linear --- Relativistic quantum field theory --- Field theory (Physics) --- Quantum theory --- Relativity (Physics) --- Physical mathematics --- Physics --- Mathematics

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Stochastic Geometry is the mathematical discipline which studies mathematical models for random geometric structures, as they appear frequently in almost all natural sciences or technical fields. Although its roots can be traced back to the 18th century (the Buffon needle problem), the modern theory of random sets was founded by D. Kendall and G. Matheron in the early 1970's. Its rapid development was influenced by applications in Spatial Statistics and by its close connections to Integral Geometry. The volume "Stochastic Geometry" contains the lectures given at the CIME summer school in Martina Franca in September 1974. The four main lecturers covered the areas of Spatial Statistics, Random Points, Integral Geometry and Random Sets, they are complemented by two additional contributions on Random Mosaics and Crystallization Processes. The book presents an up-to-date description of important parts of Stochastic Geometry.

Stochastic geometry --- Mathematics --- Physical Sciences & Mathematics --- Mathematical Statistics --- Mathematics. --- Math --- Convex geometry. --- Discrete geometry. --- Differential geometry. --- Probabilities. --- Probability Theory and Stochastic Processes. --- Convex and Discrete Geometry. --- Differential Geometry. --- Science --- Probability --- Statistical inference --- Combinations --- Chance --- Least squares --- Mathematical statistics --- Risk --- Differential geometry --- Geometry --- Combinatorial geometry --- Distribution (Probability theory. --- Discrete groups. --- Global differential geometry. --- Geometry, Differential --- Groups, Discrete --- Infinite groups --- Distribution functions --- Frequency distribution --- Characteristic functions --- Probabilities --- Discrete mathematics --- Convex geometry . --- Distribution. --- Stochastic geometry - Congresses